Trigonometry: past paper questions
Real questions on trigonometry
The newest 19 of 19 written questions. Open one to see it on the real paper.
- 9709/22 · October/November 2025 · Q2[5]
5-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/23 · October/November 2025 · Q4[5]
5-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · May/June 2025 · Q4[6]
6-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · May/June 2025 · Q6a[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · May/June 2025 · Q6b[2]
2-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/21 · October/November 2024 · Q7a[4]
4-mark “Prove” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/21 · October/November 2024 · Q7b[4]
4-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/21 · October/November 2024 · Q7c[3]
3-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2024 · Q7a[3]
3-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2024 · Q7b[3]
3-mark “Give” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · May/June 2024 · Q7a[3]
3-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · May/June 2023 · Q4[5]
5-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/33 · October/November 2021 · Q5[5]
5-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/33 · October/November 2021 · Q6a[5]
5-mark “Give” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/33 · October/November 2021 · Q6b[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/22 · May/June 2021 · Q3[6]
6-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/22 · May/June 2021 · Q7a[1]
1-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/22 · May/June 2021 · Q7b[2]
2-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/23 · May/June 2021 · Q3[6]
6-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper →
What examiners said
Many candidates understood that they needed to convert the given equation to an equation in a single cosine function. A minority of candidates obtained a correct equation. The common incorrect approaches were: – to use an incorrect ‘half angle’ formula thinking that cos 21 x = 21 cos2 x − 1. – to use the double angle formula and covert to expressions using cos x and cos 41 x . – to use u = cos 21...
— Examiner report, May/June 2023, 9709/32 Q4 (Cambridge)
Most candidates gained either 4 or 5 marks on this question. Those who gained 4 marks often either forgot the solution from sin θ = −1 or did not realise that the solution from the other sin θ value also had an answer in the second quadrant: 180° − 56.4°.
— Examiner report, October/November 2021, 9709/33 Q5 (Cambridge)
Many candidates produced fully correct solutions to this trigonometrical problem. It was rare to see an incorrect expansion of cos(x − 60°) and values of sin(60°) and cos(60°) were almost always exact and correct. The main error seen was expressing R as a decimal rather than an exact value.
— Examiner report, October/November 2021, 9709/33 Q6(a) (Cambridge)
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